Massachusetts is investigating whether top retail brokerage firms send customer buy and sell orders to exchanges that offer the brokers kickbacks and whether that practice prevents ordinary investors from getting the best price for their trades.

In a statement on Tuesday, the state's securities regulator, William Galvin, said he had requested information from seven of the biggest U.S. brokers, including Boston-based Fidelity Investment's brokerage division.

Exchanges have long paid traders for orders, something critics call kickbacks but what the industry calls rebates. As electronic trading proliferated in the last decade and the number of exchanges and trading sites blossomed, rebating became a strategy by exchanges to draw trading volume. But critics, including money managers, have complained that the practice hurts ordinary investors by creating the wrong incentives, namely, the broker or trader is motivated to pick the exchange that offers a rebate versus the one that would get the best price for a particular trade.

Galvin, who is Massachusetts' Secretary of the Commonwealth, pointed to a recent opinion column in The New York Times, penned by Yale Law School's Jonathan Macey and Yale Chief Investment Officer David Swensen that said customers don't get the best price when brokers choose exchanges for the rebates they offer.

"My office is looking into the veracity of these assertions and whether the brokers are meeting their best execution obligation to their customers," Galvin said in a statement on Tuesday announcing the investigation. "If financial rebates or kickbacks create a conflict that results in less than the best deal for the investors, this practice must stop."

Many retail brokerage firms send their customer orders to other firms known in the business as wholesalers or market makers, and some of those arrangements include payments. Schwab, for example, sent 29 percent of its customer orders to the trading firm KCG to be executed in the second quarter, receiving an average of less than $.0009 a share for the orders, according to its recent regulatory filing. It sent 27 percent to the trading arm of the hedge fund Citadel in a similar arrangement.

E-Trade sent 41 percent of its orders to a firm called G1, a former affiliate that pays it an average of $.0001 a share for orders, according to its recent regulatory filing. E-Trade also sends orders to Citadel Securities, Bats, KCG and Citi, among others.

The practice has long been debated in the securities industry, where some question whether the market making firms are helping to get the best price for each trade for the relatively small amount they pay out for the orders.

"This is a global dialogue," said Spencer Mindlin, a capital markets analyst at Aite Group. "There are good arguments on both sides, but the question is how will the regulators step in and when is it appropriate to step in? It's like pulling a thread on a sweater."

A spokesperson for TD Ameritrade told CNBC it was company practice to not comment on regulatory inquiries. A spokesman for Fidelity said "we are still reviewing the inquiry and it is too early to comment." Scottrade said it does not have any information to provide regarding this matter.

Edward D. Jones said it had not received Galvin's letter so has no comment, and Schwab said it is reviewing the letter, adding it "takes its responsibility to provide clients with best trade execution very seriously and has a strong track record of meeting those obligations."

Representatives of the other brokerages weren't immediately available.